Google Earth allows you to view many prominent buildings in 3d. Imagine that you are
the maths wiz at Google whose job it is to create a 3d image of our cube for Google Earth.
This means that you have to and coordinates of the corners of the square A;B;C;D visible
from the top, as well as the coordinates of the points A0;B0;C0;D0 at which four edges of
the Cube meet the ground. As indicated in the rst picture, A is supposed to be connected
to A0 by such an edge, and similarly for B and B0, C and C0, and D and D0.
You are new to this job and you are supposed to base your work on your predecessor's
work (who got fired yesterday). His notes are a terrible mess, but it is clear that he started
modelling the cube by letting the (
at) ground coincide with the xy-plane and having the
y-axis point West and the x-axis point North. His notes don't tell you where the origin of
his coordinate system is supposed to be, but wherever it may be, in this coordinate system
B = (26:3720; 35:3768; 13:1872), B0 = (24:9863; 31:7691; 0), D = (54:0957; 24:7282; 13:1872):
Your job also involves guring out how long the sides of the cube are; how long the four
segments AA0;BB0;CC0;DD0 are; how large the area of the quadrilateral A0;B0;C0;D0 is;
and, finally, what the volume of the part of the cube that sits above the ground is.